Preface to the First Edition The present book on Mathematics has been written for the benefit of the students pursuing studies of first semester B.E. B.Tech in various Engineering Colleges and Universities. The aim of publishing the book is to provide easy and better understanding of the subjects to all concerned. The subject matter has been dealt with comprehensively and discussed lucidly for the easy understanding of the students. The distinguishing feature of the book is that a large number of typical problems selected from recent question papers of various Universities and Engineering Colleges have been solved to make the students familiar with the recent style of the papers set in the University Examinations. We are grateful to our friends, faculty members and well wishers for encourangement, help and co-operation given for the publication of this book. We are specially indebted to our most respected Dr. O.P. Bhalla, the Hon ble President of MREI, Faridabad for all his elderly graces and blessings for writing the present book. The authors take this opportunity to express their deep sense of gratitude to Dr. D.S. Kumar, Executive Director, MREI for his able guidance and invaluable suggestions for the publication of the book. The authors are also grateful to the members of M s Manav Rachna Publishing House Pvt. Ltd., Delhi for the efforts they have put in to bring out the book in a short time. All efforts have been made to make the book useful to the students and keep the book free from errors, even then we shall be grateful if you bring to our notice any mistake you come across. All suggestions regarding the improvement of the book will be highly appreciated and gratefully acknowledged.
Dedicated to Our Parents
Partial Differentiation 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11
Dependent and independent variables 1 Partial derivatives 1 Which variable is to be treated as constant 12 Homogeneous functions 16 Euler s theorem on homogeneous function of two variables 16